A construction done using only a straightedge. The Poncelet-Steiner theorem proves that all constructions possible using a compass and straightedge are possible using a straightedge alone, as long as a fixed circle and its center, two intersecting circles without their centers, or three nonintersecting circles are drawn beforehand. For example, the centers of two intersecting circles can be found using a straightedge alone (Steinhaus 1999, p. 142).
Steiner Construction
See also
Circle-Circle Intersection, Geometric Construction, Mascheroni Construction, Matchstick Construction, Neusis Construction, Poncelet-Steiner Theorem, StraightedgeExplore with Wolfram|Alpha
References
Dörrie, H. "Steiner's Straight-Edge Problem." §34 in 100 Great Problems of Elementary Mathematics: Their History and Solutions. New York: Dover, pp. 165-170, 1965.Rademacher, H. and Toeplitz, O. The Enjoyment of Mathematics: Selections from Mathematics for the Amateur. Princeton, NJ: Princeton University Press, p. 204, 1957.Steiner, J. Geometric Constructions with a Ruler, Given a Fixed Circle with Its Center. Translated from the first German ed. (1833). New York: Scripta Mathematica, 1950.Steinhaus, H. Mathematical Snapshots, 3rd ed. New York: Dover, 1999.Referenced on Wolfram|Alpha
Steiner ConstructionCite this as:
Weisstein, Eric W. "Steiner Construction." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SteinerConstruction.html